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Search: id:A125761
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| A125761 |
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Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 1). |
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6
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| 1, 1, 1, 2, 1, 1, 1, 1, 2, 5, 12, 6, 5, 1, 1, 1, 1, 2, 5, 12, 35, 108, 73, 76, 80, 25, 15, 15, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 1044, 1475, 2205, 2643, 983, 1050, 1208, 958, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 15980, 26548, 48766, 79579, 99860, 45898, 60433, 89890, 109424, 84312, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 245955, 458397, 948201, 1857965, 3160371, 4153971, 2217787, 3402761, 5855953, 9067535, 11402651, 9170285, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 3807508, 7710844, 17354771, 37983463
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.
Row n has 4n-3 nonzero terms.
For full lists of drawings of these polyominoes for n <= 6, see the links in A125759.
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REFERENCES
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N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 31-33.
S. Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, Math. Gaz., to appear, 2008.
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EXAMPLE
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Triangle begins:
1
1,1,2,1,1
1,1,2,5,12,6,5,1,1
1,1,2,5,12,35,108,73,76,80,25,15,15
1,1,2,5,12,35,108,369,1285,1044,1475,2205,2643,983,1050,1208,958
1,1,2,5,12,35,108,369,1285,4655,17073,15980,26548,48766,79579,99860,45898,60433,89890,109424,84312
1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,245955,458397,948201,1857965,3160371,4153971,2217787,3402761,5855953,9067535,11402651,9170285
1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,901971,3426576,3807508,7710844,17354771,37983463,...
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CROSSREFS
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Row sums give A125759. Cf. A125709, A125753, A126742, A126743.
Adjacent sequences: A125758 A125759 A125760 this_sequence A125762 A125763 A125764
Sequence in context: A106498 A093815 A093466 this_sequence A060990 A056926 A137773
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KEYWORD
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nonn,tabf
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AUTHOR
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David Applegate (david(AT)research.att.com) and njas, Feb 05 2007, Feb 14 2007
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EXTENSIONS
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Rows 5, 6, 7 and 8 from David Applegate (david(AT)research.att.com), Feb 16 2007
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